1. Field of Invention
The present invention relates to computer display techniques used in connection with data analysis, and more specifically to a method and system for displaying spectral trends in complex signals.
2. Background of the Related Art
The history of techniques developed for data analysis of biological and non-biological signals is well documented. The French mathematician and physicist Jean Baptiste Joseph Fourier originated Fourier's theorem on vibratory motion and the Fourier series around 1800. This provided a method for representing discontinuous functions by a trigonometric series. In 1938, A. M. Grass and F. A. Gibbs published “A Fourier transform of the electroencephalogram (EEG)” in the Journal of Neurophysiology. 
Prior to this pioneering work, the electrical signals produced by the brain were displayed only as signals fluctuating over time. Using the Fourier transform, a 30 second segment of EEG was redisplayed, showing the relative amount of EEG energy present at different frequencies. This “pre-computer” era application used a combination of photographic, mechanical, and electronic apparatus to construct a graphical representation of the Fourier transform.
In the later half of the 20th century, the development of the digital computer greatly simplified the conversion of biological EEG signals into their corresponding frequency spectra. In 1965, J. W. Cooley and J. W. Tukey published “An algorithm for the machine computation of complex Fourier series” in Mathematical Computation. Their algorithm, known as the Fast Fourier Transform (FFT), reduced to practice an algorithm that was practical for computing the frequency spectrum of any digitized signal. Many people, research publications, and text books have described methods for calculating the frequency spectrum of a signal. The complicated nature of the FFT, which has many subtleties that cannot be ignored, is well documented in such references.
From the late 1960s through the late 1980s, many researchers were using digitized EEGs, and publishing a wide variety of analyses, including spectral analysis. In the late 1980s through the early 1990s, most of the major electroencephalograph manufacturers introduced digital electroencephalographs. For example, Schwartzer GmbH (1988), Nihon Kohden (1991), Astromed-Grass (now Grass-Telefactor), Nicolet Biomedical (now Viasys), Stellate Systems, Bio-logic Systems, Cadwell Laboratories, Oxford Instruments, all offered products. With the explosion of digital electroencephalographs, software for displaying and processing EEG also emerged. Products were offered, for example, by Persyst Development Corp. and MEGIS Software GmbH.
The techniques for calculating or displaying the spectral content of a signal are generally applied to a short and/or finite segment of data. EEG data is often collected for longer time segments, such as many hours or days. Compressed Spectral Array (CSA) is one technique that has been used to display spectral data over longer segments of time.
In 1976, G. Astaldi et. al. published “Clinical use of “compressed spectral array” in Riv. Neurology. The CSA technique takes individual power spectral density graphs or “frames”, and “stacks” a whole sequence of them in front of each other, with a slight vertical and/or horizontal shift between each frame. The effect is a pseudo three-dimensional visual effect; like looking at a mountain landscape or a contour map, with time running along one axis, and frequency running along a second axis. The CSA technique can use color or gray scales to highlight the individual lines, but that is not required. The CSA technique is effective for visualizing spectral changes over moderate time periods, but tends to be uninterpretable over very long time periods. CSA also requires a lot of display screen space.
In 1987, M. Salinsky introduced the technique of displaying EEG using color density spectral array (cDSA) in an article called “Representation of sleep stages by color density spectral array” in Electroencephalogr Clin. Neurophysiol. cDSA maps the logarithm of the EEG power in each frequency bin and at each epoch, or time period, to a color. For example, red could represent the highest level, orange somewhat less, and so on, through the color spectrum, yellow, green, blue, and violet, with violet being the lowest level. The cDSA technique can also use gray scale mapping instead of color mapping, but shows changes more strikingly in color. Since its introduction, many EEG manufacturers have adopted cDSA as a tool for displaying long-term trends in EEG data (for example, Persyst, Nihon Kohden, Viasys-Nicolet, MEGIS, Cadwell, and SpaceLabs).
Currently, cDSA is the method widely used within the industry to display long term (hours to days in time) biological signals such as spectral EEG data. Unfortunately, cDSA display is limited by the nature of the signals being analyzed. Specifically, the power in the EEG signal drops precipitously as frequency increases.
In standard cDSA display, the low frequencies are red in color, and the color gradually shifts through the color spectrum to orange, yellow, etc., to violet, as the frequency of the signal increases. While it is possible to see changes in the cDSA display over longer time periods, the changes are not particularly sensitive to changes in the relative spectral content of the EEG signal. Rather, the changes are PRIMARILY sensitive to the overall amplitude of the EEG signal, with a very secondary sensitivity to changes in the shape of the spectral density curves. This drop in spectral power is commonly referred to as a “1/f power law”, because the power tends to drop proportional to the frequency, f, raised to a power.
This limitation of the cDSA display, due to the drop in spectral signal power, is overcome by the method for display of the present application, which is referenced as the “modified color density spectral array” (mcDSA) or “modified gray density spectral array” (mgDSA) or as the closely related “modified compressed spectral array” (mCSA). Additionally, standard spectral analysis techniques are all improved and extended by the present method of display disclosed here.